Title: A novel secondary code acquisition algorithm for the BDS‐3 B1C signal
Abstract: IET Radar, Sonar & NavigationVolume 15, Issue 9 p. 1061-1072 ORIGINAL RESEARCH PAPEROpen Access A novel secondary code acquisition algorithm for the BDS-3 B1C signal Tongsheng Qiu, Tongsheng Qiu orcid.org/0000-0002-4410-1263 National Space Science Center, Chinese Academy of Sciences, Beijing, China College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this authorXianyi Wang, Corresponding Author Xianyi Wang [email protected] National Space Science Center, Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, China Correspondence Xianyi Wang, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected] for more papers by this authorQifei du, Qifei du National Space Science Center, Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this authorYueqiang Sun, Yueqiang Sun National Space Science Center, Chinese Academy of Sciences, Beijing, China College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this authorZhuoyan Wang, Zhuoyan Wang National Space Science Center, Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this author Tongsheng Qiu, Tongsheng Qiu orcid.org/0000-0002-4410-1263 National Space Science Center, Chinese Academy of Sciences, Beijing, China College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this authorXianyi Wang, Corresponding Author Xianyi Wang [email protected] National Space Science Center, Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, China Correspondence Xianyi Wang, National Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China. Email: [email protected] for more papers by this authorQifei du, Qifei du National Space Science Center, Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this authorYueqiang Sun, Yueqiang Sun National Space Science Center, Chinese Academy of Sciences, Beijing, China College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this authorZhuoyan Wang, Zhuoyan Wang National Space Science Center, Chinese Academy of Sciences, Beijing, China Beijing Key Laboratory of Space Environment Exploration, National Space Science Center, Beijing, China Key Laboratory of Science and Technology on Space Environment Situational Awareness, Chinese Academy of Sciences, National Space Science Center, Beijing, ChinaSearch for more papers by this author First published: 13 May 2021 https://doi.org/10.1049/rsn2.12097Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The BDS-3 recently started broadcasting a new civil B1C signal to provide open services for global users, which brings benefits to GNSS-based applications. The BDS-3 B1C signal modulates a long secondary code on the primary code in the pilot component, and it is useful to acquire the secondary code so as to extend coherent integration time when acquiring weak BDS-3 B1C signals. However, the long secondary code of the BDS-3 B1C signal puts FFT-based and multi-hypothesis-based secondary code acquisition methods in trouble from the high computational burden. Therefore, the authors propose a novel secondary code acquisition algorithm called the partial correlation method (PCM) for the BDS-3 B1C signal. The PCM acquires the secondary code in three steps to reduce the complexity and acquisition time, and it supports up to 110 ms coherent integration and can be applied for the case of C / N 0 ≥ 25 dB - Hz , which satisfies most cases. Further, a matched-filter-based architecture of the PCM is presented. Additionally, the characteristic length vector to determine the secondary code chip position quickly is proposed, which is better than the existing characteristic length method. Finally, experimental results based on real BDS-3 B1C signals data show that the proposed PCM is effective. 1 INTRODUCTION The Chinese third-generation BeiDou Navigation Satellite System (BDS-3) is a global navigation satellite system (GNSS), and the BDS-3 recently started broadcasting a new civil B1C signal to provide open services for global users. Similar to other modern GNSS signals, the BDS-3 B1C signal also adopts a tiered code architecture and modulates a long secondary code on the primary code in the pilot component. Although the long secondary code provides an increased cross-correlation property [1, 2], the longer the secondary code, the higher the complexity of secondary code acquisition methods, and the more secondary code chips will need acquiring to determine its chip position so as to conduct bit synchronisation [3]. Moreover, acquiring the secondary code is an effective method to extend the coherent integration time when acquiring weak signals [4, 5], especially the weak BDS-3 B1C signal, because the pilot component power of the BDS-3 B1C signal accounts for three-quarters of the signal power. Hence, low-complexity long secondary code acquisition algorithm is a heated topic about acquiring weak BDS-3 B1C signals. At present, there are two main categories of secondary code acquisition algorithms. Since the secondary code chip-sign transition restricts the extension of coherent integration time, the first type of algorithm is to sequentially or simultaneously test all possible symbol combinations based on the consecutive correlated results of a primary code period [1, 6-11]. However, since the number of possible symbol combinations increases exponentially with the growth of secondary code chips, these methods are only adopted in the case of short coherent integration time. Although some algorithms claimed to be able of reducing the theoretical number of operations when testing all possible symbol combinations [3, 12, 13], either the algorithm architecture complexity and processing time in terms of implementation in hardware have not been reduced, or only a short secondary code can adopt it and with signal-to-noise ratio (SNR) loss. Since the secondary code is periodic and entire chips in a secondary code period are prior knowledge, the second type of algorithm is based on FFT and IFFT to perform the parallel search of all candidate secondary code phases [12-16]. In terms of the BDS-3 B1C signal, the primary code contains 10,230 chips in a period of 10 ms, and the secondary code contains 1800 chips in a period of 18 s. As a consequence, the FFT-based secondary code acquisition algorithms have an extremely heavy computational burden for both software and hardware when acquiring the weak BDS-3 B1C signal. Therefore, these FFT-based secondary code acquisition algorithms are not suitable for the BDS-3 B1C signal. Consequently, the authors propose a novel secondary code acquisition method called the partial correlation method (PCM) to acquire the long secondary code of the BDS-3 B1C signal so as to acquire the weak BDS-3 B1C signal. The PCM acquires the secondary code in three steps. In terms of acquiring N secondary code chips, the first step is to acquire the first half of N secondary code chips, and the second step is to acquire the other half. The final step is to coherently combine two results obtained by the previous two steps to form the final decision statistic. As a result, the PCM significantly reduces the number and length of possible symbol combinations, even if extending the coherent integration time up to 110 ms (i.e. N = 11), which significantly reduces the acquisition algorithm complexity and acquisition time and simplifies the acquisition architecture. Additionally, bit synchronisation is dependent on the determination of secondary code chip position, and therefore the authors propose the characteristic length vector to determine the secondary code chip position quickly, which is better than the present characteristic length method [7, 17]. The BDS-3 B1C signal is briefly described in Section 2. Then, primary code acquisition principles of the BDS-3 B1C signal are introduced in Section 3. In Section 4, the proposed secondary code acquisition algorithm PCM is explained in detail. Based on the PCM, the acquisition architecture is presented in Section 5, and the performance evaluation of the PCM is conducted in Section 6. Afterwards, the characteristic length vector is calculated in Section 7. Experiments based on real BDS-3 B1C signals data are subsequently carried out to verify the PCM in Section 8. Finally, some summarising conclusions are drawn in Section 9. 2 BDS-3 B1C SIGNAL The BDS-3 B1C signal is a modern GNSS signal, which contains two components, the data component and pilot component, respectively. The data component modulates data bits on the primary code, and the pilot component modulates a secondary code on the primary code. The secondary code of the BDS-3 B1C signal is the Weil code, which contains 1800 chips in a period of 18 s. Each secondary code chip strictly aligns with one period of primary code, and the primary code contains 10,230 chips in a period of 10 ms. Moreover, every pseudo random noise (PRN) number corresponds to a unique secondary code. In comparison to other secondary codes, the secondary code of the BDS-3 B1C signal is really a long secondary code as Table 1 shows. TABLE 1. Secondary code characteristics Signal Primary Code Secondary Code Length Period Length Period (Chip) (ms) (Chip) (ms) GPS L5 10,230 1 20 20 Galileo E1 4092 4 25 100 Galileo E5 10,230 1 100 100 BDS-3 B1C 10,230 10 1800 18,000 As Table 2 shows, the pilot component of the BDS-3 B1C signal adopts the QMBOC(6,1,4/33) modulation mode that consists of two parts, BOC(1,1) and BOC(6,1), respectively. On one hand, the power of the BOC(1,1) accounts for 29 / 44 of the total power of the BDS-3 B1C signal. On the other hand, the sub-carrier frequency of the BOC(1,1) is 1.023 MHz, and it is less than that of the BOC(6,1), which indicates the acquisition engine designed for the BOC(1,1) generally has lower complexity than that designed for the BOC(6,1). Therefore, we merely consider the BOC(1,1) of the pilot component herein. TABLE 2. Characteristics of BDS-3 B1C signal Signal BDS-3 B1C Component Data Pilot Modulation mode BOC(1,1) QMBOC(6,1,4/33) BOC(1,1) BOC(6,1) Phase 0 90 0 Power ratio One-quarter 29/44 1/11 Abbreviation: BDS, beidou navigation satellite system; BOC, binary offset carrier; QMBOC, quadrature multiplexed binary offset carrier. 3 PRIMARY CODE ACQUISITION First of all, attention here is mainly paid to the secondary code acquisition algorithm for the BDS-3 B1C signal. Hence, detailed information about the primary code acquisition method is not the focus. To illustrate the proposed PCM, the two-dimension search method based on short-time coherent integration plus a FFT is considered [18-20], as Figure 1 shows. It should be noted, that other search methods such as serial search [21], parallel frequency search [22], and parallel code search [23], are also suitable for primary code acquisition and cooperation with the PCM. Additionally, the BPSK-like method [24] is applied to achieve unambiguous acquisition of the BOC(1,1). FIGURE 1Open in figure viewerPowerPoint Diagram block of the acquisition architecture based on partial correlation method (PCM) to acquire the weak BDS-3 B1C signal Generally, the discrete-time BOC(1,1) signal of the BDS-3 B1C signal pilot component at the output of the radio frequency front-end is given by: r [ n ] = 2 P . s [ n − τ ] . c [ n − τ ] . s i g n [ s i n ( 2 π f s c n T s ) ] . s i n [ 2 π ( f I F + f d ) n T s + φ 0 ] + η [ n ] (1)where P represents signal power, s [ n ] denotes the secondary code, c [ n ] is the primary code, s i g n [ s i n ( 2 π f s c n T s ) ] is the sub-carrier, f s c = 1.023 MHz , τ represents the path delay, f I F is the nominal intermediate frequency (IF), f d represents the Doppler frequency, φ 0 is the initial phase, η [ n ] denotes the additive white Gaussian noise with two-side noise power spectrum density (PSD) of N 0 / 2 W / Hz , and T s is the sampling interval. Subsequently, the local generated complex exponential carrier e x p [ − j 2 π ( f I F + f s c ) n T s ] and primary code replica c [ n − τ ^ ] are generated to correlate with r [ n ] . In addition, the short-time correlation time is T c , and T c = N p T s . Taking T p the period of the primary code into account, T p = L T c = 10 ms . In order to simplify the expression, the low pass filter (LPF) designed for the BPSK-like method is assumed as an ideal finite impulse response (FIR) filter. After filtering operation of the LPF and the short-time coherent integration, the l -th result is obtained as: G ( τ ^ , l ) = ∑ n = l N p ( l + 1 ) N p − 1 L P F { r [ n ] . e x p [ − j 2 π ( f I F + f s c ) n T s ] } . c [ n − τ ^ ] = 2 p . R ( Δ τ ) 2 . s i n ( π f d T c ) s i n ( π f d T s ) . s [ l ] . e x p { j [ π f d ( 2 l N p + N p − 1 ) T s + φ 0 ] } + ξ [ l ] (2)where Δ τ = τ − τ ^ , R ( Δ τ ) represents the auto-correlation function (ACF) of the primary code, and ξ [ l ] is the present complex noise item. Afterwards, a N F F T -points zero-padding FFT is used to conduct parallel Doppler frequency search, and N F F T = 2 m ( m ∈ N + ). To avoid the scalloping loss, N F F T ≥ 2 L , and the number of padding zeros is N F F T − L . Consequently, the output of i -th FFT operation is calculated as: F i ( τ ^ , f d ^ ) = ∑ l = i L ( i + 1 ) L − 1 G ( τ ^ , l ) . e x p ( − j 2 π N F F T k l ) = 2 p . R ( Δ τ ) 2 . s i n ( π f d T c ) s i n ( π f d T s ) . s i n [ π Δ f d T p ] s i n [ π Δ f d T c ] . s i . e x p ( j φ i ) + ζ i = A 0 . s i . e x p ( j φ i ) + ζ i (3)where Δ f d = f d − f d ^ , and f d ^ = k / ( N F F T . T c ) , φ i = φ 0 + π f d ( N p − 1 ) T s + π Δ f d ( 2 i L + L − 1 ) T c , ζ i is the present noise item. Considering the long-time coherent integration up to 110 ms, the Doppler frequency estimation deviation Δ f d should be generally within a small range of − 2.5 Hz ∼ 2.5 Hz . Moreover, it should be noted that Doppler compensation may be necessary for long-time coherent integration. As the main focus here is on the secondary code acquisition, detailed information about Doppler compensation can be found in [25]. According to the central limit theorem, ζ i in Equation (3) is a complex Gaussian random variable with zero mean and variance 2 σ 2 . The real and imaginary parts of the ζ i are independent and have zero mean and equal variance σ 2 . Therefore, the carrier-to-noise ratio ( C / N 0 ) in dB - Hz ( dB*Hz ) is given by: C / N 0 = 10 . l o g ( A 0 2 2 σ 2 . 1 T p ) = 10 . l o g ( A 0 2 2 σ 2 ) + 20 (4) C / N 0 is a key parameter to evaluate the performance of the PCM. 4 SECONDARY CODE ACQUISITION As previously discussed, the secondary code of the BDS-3 B1C signal contains 1800 chips in a period of 18 s , that is N s = 1800 . In terms of acquiring N secondary code chips, considering the ambiguity of the secondary code chip sign, the number of possible symbol combinations is given by: M = m i n { 2 N − 1 , N s } (5)when N ≤ 11 , M = 2 N − 1 . The case of N ≤ 11 means the coherent integration time can reach up to 110 ms, which satisfies most of the weak signal situations when considering the optional non-coherent integration method after coherent integration. Hence, the focus here is only on the case of N ≤ 11 . As previously discussed, the PCM acquires the secondary code in three steps, and then it is given by: { M 1 = 2 N 1 − 1 , N 1 = c e i l ( N / 2 ) M 2 = 2 N 2 − 1 , N 2 = N − N 1 (6) According to Equation (3), N consecutive realisations of F i ( τ ^ , f d ^ ) are obtained and expressed in vector: F = [ F 0 ( τ ^ , f d ^ ) , F 1 ( τ ^ , f d ^ ) , … , F N − 1 ( τ ^ , f d ^ ) ] T (7)where the input secondary code sequence is S g , and S g = [ s 0 , g , s 1 , g , … , s N − 1 , g ] T . It is clear that S g has 2 N − 1 possibilities when considering the ambiguity of chip sign, that is, 1 ≤ g ≤ 2 N − 1 . Then, based on Equation (6), Equation (7) can be rewritten as: F = [ F 1 T , F 2 T ] T (8)where F 1 = [ F 0 ( τ ^ , f d ^ ) , … , F N 1 − 1 ( τ ^ , f d ^ ) ] T , and F 2 = [ F N 1 ( τ ^ , f d ^ ) , … , F N − 1 ( τ ^ , f d ^ ) ] T . At this point, S g = [ S u T , S v T ] T , or S g = [ S u T , − S v T ] T . S u = [ s 0 , u , s 1 , u , … , s N 1 − 1 , u ] T ( 1 ≤ u ≤ M 1 ) and S v = [ s 0 , v , s 1 , v , … , s N 2 − 1 , v ] T ( 1 ≤ v ≤ M 2 ). It should be noted that the logic values {'0', '1'} of secondary code chips are separately transformed into digital values {1, −1} during acquisition. Without loss of generality, S v = [ 1,1,1 , … ] ( S v = [ ′ 0 ′ , ′ 0 ′ , ′ 0 ′ , … ] ), and then − S v = [ − 1 , − 1 , − 1 , … ] ( − S v = [ ′ 1 ′ , ′ 1 ′ , ′ 1 ′ , … ] ). Therefore, − S v means the transition of polarity of the secondary code sequence S v . 4.1 First step of the PCM To acquire first N 1 secondary code chips, a total of M 1 possible symbol combinations are generated: Ma t 1 = [ S ^ 1 , S ^ 2 , … , S ^ M 1 ] T = [ s ^ 0,1 s ^ 1,1 s ^ 0,2 s ^ 1,2 ⋯ s ^ N 1 − 1,1 ⋯ s ^ N 1 − 1,2 ⋮ ⋮ s ^ 0 , M 1 s ^ 1 , M 1 ⋱ ⋮ ⋯ s ^ N 1 − 1 , M 1 ] (9)where S ^ j ( 1 ≤ j ≤ M 1 ) is the j -th candidate symbol combination, and S ^ j = [ s ^ 0 , j , s ^ 1 , j , … , s ^ N 1 − 1 , j ] T . Subsequently, secondary code correlation results are calculated as: X = [ x 1 ( τ ^ , f d ^ ) x 2 ( τ ^ , f d ^ ) ⋮ x M 1 ( τ ^ , f d ^ ) ] = Ma t 1 · F 1 (10)where x j ( τ ^ , f d ^ ) = ∑ i = 0 N 1 − 1 s ^ i , j . F i ( τ ^ , f d ^ ) = A . R j , u . e x p ( j φ ) + ζ j (11)and R j , u = S ^ j T . S u = ∑ i = 0 N 1 − 1 s ^ i , j . s i , u (12) Also in Equation (11), A = A 0 . s i n [ π Δ f d T p N 1 ] s i n [ π Δ f d T p ] , R j , u represents the cross-correlation results between the local S ^ j and the input secondary code sequence S u , φ is the residual carrier phase, and ζ j is present noise item. Finally, the optimal estimate of the first step is generally given by [26]: | x u ( τ ^ , f d ^ ) | 2 = max j { | x j ( τ ^ , f d ^ ) | 2 } (13) Hence, S ^ u is taken as the optimal estimate of the first step. 4.2 Second step of the PCM To acquire the rest of the N 2 secondary code chips, a total of M 2 possible symbol combinations are generated: Ma t 2 = [ S ^ 1 , S ^ 2 , … , S ^ M 2 ] T = [ s ^ 0,1 s ^ 1,1 s ^ 0,2 s ^ 1,2 ⋯ s ^ N 2 − 1,1 ⋯ s ^ N 2 − 1,2 ⋮ ⋮ s ^ 0 , M 2 s ^ 1 , M 2 ⋱ ⋮ ⋯ s ^ N 2 − 1 , M 2 ] (14)where S ^ h ( 1 ≤ h ≤ M 2 ) is the h -th candidate symbol combination, and S ^ h = [ s ^ 0 , h , s ^ 1 , h , … , s ^ N 2 − 1 , h ] T . Similar to the first step, secondary code correlation results are calculated as: Y = [ y 1 ( τ ^ , f d ^ ) y 2 ( τ ^ , f d ^ ) ⋮ y M 2 ( τ ^ , f d ^ ) ] = Ma t 2 . F 2 (15) Finally, the optimal estimate of the second step is generally given by [26]: | y v ( τ ^ , f d ^ ) | 2 = max h { | y h ( τ ^ , f d ^ ) | 2 } (16) Hence, S ^ v is taken as the optimal estimate of the second step. 4.3 Third step of the PCM The third step is to coherently combine two results obtained by the previous two steps to form the final decision statistic. First, two candidate estimates of the input secondary code sequence separately corresponding to hypothesis H 1 and H 2 are given by: { S g = S ^ 1 = [ S ^ u T , S ^ v T ] T , H 1 S g = S ^ 2 = [ S ^ u T , − S ^ v T ] T , H 2 (17) Based on Equation (17), two candidate decision statistics z 1 and z 2 are obtained as: { z 1 ( τ ^ , f d ^ ) = x u ( τ ^ , f d ^ ) + y v ( τ ^ , f d ^ ) , H 1 z 2 ( τ ^ , f d ^ ) = x u ( τ ^ , f d ^ ) − y v ( τ ^ , f d ^ ) , H 2 (18) Afterwards, the final optimal estimate is generally given by [26]: | z w ( τ ^ , f d ^ ) | 2 = max i { | z i ( τ ^ , f d ^ ) | 2 } (19) Eventually, the optimal estimate of the input secondary code sequence is S ^ w ( w ∈ { 1,2 } ). The | z w ( τ ^ , f d ^ ) | 2 is compared with the predefined threshold β to make acquisition decisions. The predefined threshold β of the PCM is unquestionably the same as that of the multi-hypothesis based method (MHM) in terms of the same false-alarm probability. 5 ARCHITECTURE OF THE PCM To reduce the architecture complexity and hardware resources consumption, the architecture of the PCM is based on an inverse-structure matched filter. According to the method of constructing the m-sequence proposed in paper [1], as Figure 2 shows, two m-sequences S m , 1 and S m , 2 are first constructed that separately correspond to Ma t 1 and Ma t 2 . The S m , 1 contains 2 N 1 − 1 elements, and the S m , 2 contains 2 N 2 − 1 elements. Based on S m , 1 and S m , 2 , two extended combining sequences S e x t , 1 and S e x t , 2 are established respectively, as shown in Figure 3. FIGURE 2Open in figure viewerPowerPoint Figure showing the method of constructing the m-sequence FIGURE 3Open in figure viewerPowerPoint Drawing showing establishment of the extended combining sequence based on m-sequence Finally, the architecture of the PCM is as shown in Figure 4. The circular correlation between S e x t , 1 and F 1 , and the circular correlation between S e x t , 2 and F 2 are carried out step by step so as to test all possible symbol combinations. FIGURE 4Open in figure viewerPowerPoint Diagram block of the proposed partial correlation method 6 PERFORMANCE OF THE PCM Performance analyses of the PCM mainly include three aspects, hardware resources consumption, acquisition time, and detection probability, which are based on comparisons between the PCM and the MHM. As far as the MHM, m-sequence S m and extended combining sequence S e x t are also established by above-mentioned methods, and then, similar to the architecture of the PCM, the architecture of the MHM is as shown in Figure 5. FIGURE 5Open in figure viewerPowerPoint Diagram block of the existing multi-hypothesis-based method (MHM) 6.1 Hardware resources consumption and acquisition time Hardware resources consumption is one of the most important aspects in terms of a highly complex weak-signal acquisition engine [27]. As Figure 4 shows, the matched filter in the architecture of the PCM contains N 1 correlators, and the matched filter in the architecture of the MHM contains N correlators, as shown in Figure 5. On one hand, every correlator in the matched filter is usually implemented by an accumulator in practice, which is the main source of matched-filter complexity. On the other hand, as Equation (6) shows, N 1 is approximately half of N . As a consequence, the PCM consumes less hardware resources than the MHM. Acquisition time is another key factor used to evaluate the performance of an acquisition algorithm [28]. At this point, acquisition time is mainly concerned with secondary code correlation operations. The time to load new data and the latency in the processing are usually not considered. In terms of the PCM, the length of S e x t , 1 is 2 N 1 − 1 + N 1 − 1 , and the length of S e x t , 2 is 2 N 2 − 1 + N 2 − 1 . Hence, the acquisition time of the PCM is given by: T P C M = ( 2 N 1 − 1 + N 1 − 1 ) + ( 2 N 2 − 1 + N 2 − 1 ) f c l k (20)where f c l k represents system clock frequency. In terms of the MHM, similarly, acquisition time is given by: T M H M = 2 N − 1 + N − 1 f c l k (21) Then, the acquisition time ratio is given by: T P C M T M H M = 2 N 1 − 1 + 2 N 2 − 1 + N − 2 2 N − 1 + N − 1 (22) As Figure 6 shows, the acquisition time of the PCM is less than that of the MHM. With the growth of N , the acquisition time ratio decreases, and the advantage of the PCM over the MHM increases. FIGURE 6Open in figure viewerPowerPoint Acquisition time of the proposed partial correlation method and the existing multi-hypothesis method (MHM) 6.2 Detection probability Firstly, both false-alarm probability and detection probability are both challenging issues concerned with secondary code acquisition, because different local symbol combinations are not independent when N ≥ 3 . Even so, some conclusions about the false-alarm probability are given by [1], and then the predefined threshold β can be obtained with given false-alarm probability. S
Publication Year: 2021
Publication Date: 2021-05-13
Language: en
Type: article
Indexed In: ['crossref', 'doaj']
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